Question

How do you integrate e^2x sin(3x)dx?

Answer 1

Use integration by parts. Btw when is this due?

Answer 2

its a revision, we cant figure it out

Answer 3

No i just meant i have to do my own hw too, so do u need this like right away or by tonite or by 2morro mornin?

Answer 4

ill just do it now

Answer 5

we would just like to know what to do with the sin(3x)

Answer 6

thanks!

Answer 7

ima write this out on paper and email it to u. what's ur email?

Answer 8

moca341@hotmail.com .. thank you :)

Answer 9

np

Answer 10

almost done...

Answer 11

great!

Answer 12

i will take separate pix and email them one by one, the whole solution won't fit lol

Answer 13

thats fine! haha

Answer 14

okay emailed it

Answer 15

ask me if u have any questions, either here or by email and Fan if I helped!

Answer 16

did u get it?

Answer 17

It helped a lot, but i dont really get it!, ill try to figure it out!
thanks a lot!

Answer 18

no, ask me which part don't you understand?

Answer 19

I think it might the place where I let that one integral be capital i

Answer 20

i dont even understand the first line, dont worry about it!

Answer 21

Oh okay so first I used integration by parts. See the stuff in the circle:
I said Let u = e^(2x), then what is du/dx?
du/dx = derivative of u = 2e^(2x), multiply both sides by dx to get:
du = 2e^(2x)dx

Answer 22

i dont see where the 1/3 cos (3x) comes from

Answer 23

Oh okay that's just the integral of Sin(3x)

Answer 24

I will work it out here:
After that I said let dv/dx = Sin(3x), well then what's V? v is the integral of dv/dx with respect to x.
V = Integral(dv/dx, dx)
\[v = \int\limits_{}^{}Sin(3x)dx\]

Answer 25

Here you have to use a simple substitution:
Let a = 3x; then da = 3 dx. Now you have 3x in your integral, but you still need a 3 in front of dx. To do so, multiply and divide by 3, same as multiplying by 1

Answer 26

ok, i get it, thanks a lot!

Answer 27

\[v = \int\limits_{}^{}Sin(3x)*(3/3)*dx = (1/3) *\int\limits_{}^{}Sin(3x)*3*dx\]

Answer 28

Now you have both a and da; your integral simplifies to:
\[(1/3)\int\limits_{}^{}Sin(a)*da\]

Answer 29

that's it then integrate as u would a regular sin and in the end replace a by 3x